Question: A motorist covers a distance of 39 km in 45 min by moving at a speed of x km/h for the first 15 min, then moving at double the speed for the next 20 min and then again moving at his original speed for the rest of the journey. Then, x is equal to:

(A) 31.2
(B) 36
(C) 40
(D) 52
(E) 53

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

• A motorist covers a distance of 39 km in 45 min
• He moves at a speed of x km/h for the first 15 min,
• He moves at double speed for the next 20 min.
• He again moves at his original speed for the rest of the journey.

Find out

• The value of x.

Case 1:

As per the question, the motorist moves x km/h for the first 15 min
Therefore, the distance travelled by the motorist in the first 15 min = x ∗ 15/60 = x/4 km

Case 2:

It is given, the motorist travels 2x km/h for the next 20 min
Therefore, the distance covered by the motorist in the next 20 minutes = 2x ∗ 20/60 = 2x/3 km

Case 3:

Further, the motorist travels x km/h for the remaining time that is = 45 - (15+20) = 10 min
Therefore, the distance travelled by the motorist for the rest of his journey = x ∗ 10/60 = x/6 km

Therefore, we can say that the total distance travelled by the motorist is 39 which is equal to the sum of x/4, 2x/3 and x/6.
=> x/4 +2x/3 + x/6 = 39
Taking the LCM of the denominators it can be derived as:
=> (3x + 8x + 2x) /12 = 39
=> 13x/12 = 39
Hence, x = 39 * 12/13 = 36 kmph

Therefore, the speed of the motorist for the first 15 min is 36kmph.

Approach Solution 2:

The problem statement informs that:

Given:

• A motorist covers a distance of 39 km in 45 min.
• He moves at a speed of x km/h for the first 15 min.
• He moves at double speed for the next 20 min.
• He again moves at his original speed for the rest of the journey.

Find out

• The value of x i.e the speed of the motorist for the first 15 min.

From the given conditions of the question, an equation can be created.
Since the motorist travels at x km/h for the first 15 min, 2x km/h for the next 20 min, and x km/h for the remaining time, we can rewrite the equation as:
(15/60)(x) + (20/60)(2x) + (10/60)(x) = 39
Therefore, we can derive the equation as:
x/4 + 2x/3 + x/6 = 39
By multiplying the equation by 12, we get:
3x + 8x + 2x = 12 * 39
Hence, we can say, 13x = 12 * 39

Therefore, x = 12 * 3 = 36

Hence, the speed of the motorist for the first 15 min = 36kmph.

“A motorist covers a distance of 39 km in 45 min by moving at a speed”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions enable the candidates to boost their mathematical skills by solving quantitative problems. It tests the candidates’ numerical literacy and abilities in calculating the sums accurately. GMAT Quant practice papers help the candidates to go through different sorts of questions that will enhance their mathematical knowledge and understanding.

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